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Question
Solve for x: log 3 (tan x) = 1/2. tan x = the square root of 3
It can be seen that tan x = √3.
This means that if the far side is √3, the near side is 1.
If we know the two sides of a right triangle, the hypoteneuse can be determined from these by c² = a² + b².
We can see that c² = √3² + 1² = 3 + 1 = 4. This means that c is 2.
If you draw the triangle with √3 as the vertical side,
it can be reflected into another triangle that shares 2
as the common side. Both sides that are pointing up have length 2,
and the bottom side has length 1 + 1 from the mirror image,
so that it is also 2. Since all the sides are equal,
all the angles are equal. Since the sum of angles in a triangle
is always 180°, three equal angles each measures 60°. Now if we cut
that triangle back in half with a vertical line so that we are
looking at our starting triangle, that means we cut the top angle in
half so that it is now a 30° angle.
That's what I know as a 1-2-3 triangle.
The sides are of length 1, 2, √3 and the angle are
1, 2, 3 times 30°, which, as you can see, is 30°, 60°, 90°.
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Answers by Expert:
Scotto
Expertise
Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.
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Experience in the area: I have tutored students in all areas of mathematics for over 25 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
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Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC.
Well over 2,000 of them have been in calculus.
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I aquired well over 40 hours of upper division courses. This was well over the number that were required.
I graduated with honors in both my BS and MS degree from Oregon State University.
I was allowed to jump into a few junior level courses my sophomore year.
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I have been nominated as the expert of the month several times.
All of my scores right now are at least a 9.8 average (out of 10).
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My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.
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